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VECTORS

VECTORS. PARALLEL VECTORS. Make one value negative and add together when they are in opposite directions. ACCELERATION AND VELOCITY. V. Accelerating to the right. A. V. Decelerating to the right. A. V. Accelerating to the left. A. v. Decelerating to the left. A. RESULTANT VECTOR.

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VECTORS

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  1. VECTORS

  2. PARALLEL VECTORS Make one value negative and add together when they are in opposite directions.

  3. ACCELERATION AND VELOCITY V Accelerating to the right A V Decelerating to the right A V Accelerating to the left A v Decelerating to the left A

  4. RESULTANT VECTOR A resultant vector represents the sum of two or more vectors

  5. THE BOAT CURRENT DIRECTION OF BOAT

  6. VECTORS AT RIGHT ANGLES Magnitude: Pythagorean Theorem a2 + b2 = c2 Direction: Tan Ѳ = opposite adjacent c b a

  7. PYTHAGOREAN THEORM

  8. Ex: A bird flew 4m east then 8m north relative to the ground. What is the displacement of the bird? a2 + b2 = c2 4m2 + 8m2 = c2 16 + 64 = c2 √80 =c C= 8.94m Tan Ѳ = 8m/4m Tan Ѳ = 2 Ѳ = Tan-1 2 Ѳ=63.4⁰ Ѳ C = 8.94m@63.4⁰ NE

  9. What about the other triangles? LAW OF COSINE: c² = a² + b² − 2abcos C LAW OF SINE:

  10. c² = a² + b² − 2abcos C Ex: A deer travels 10m east then turns 45⁰ and travels 15m NE. Find the deer’s displacement. c2 = 10m2 + 15m2-2(10)(15)cos 135 c2 = 100 + 225 – (-212) c2 = 537 c = 23m 45⁰ a = c 15m= 23m SinASinCsinѲSin 135⁰ 23sinѲ = 15sin 135⁰ Ѳ = 27.5⁰ C = 23m @ 27.5 ⁰ NE

  11. Vector Components • The two perpendicular vectors that combine to form the resultant. Ay A 30° Ax

  12. Component formula’s X – component: Ax = A cosθ Y- component: Ay = A sinθ

  13. A car is displaced 300m at 30°NE from its starting position. If it followed Elm street east and then turned north on Willow Street, how far did it travel on each street? Ax = AcosѲ Ax =300m cos30 Ax = 259.8m (Elm) Ay = AsinѲ Ay = 300m sin 30 Ay = 150m (Willow) 300m Willow Elm

  14. As the angle of a resultant vector gets larger, The x component decreases The y component increases Y Y θ θ X X

  15. At 45 degrees the x component is equal to the y component. Y 45° X

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